Modeling problen with edgings
Simple answer: model them.

There are many different kinds of seams on various furniture so it is essential to have good reference photos and see clearly how they look so you can then decide what will be the most appropriate method for modelling them. The ones in the picture seem to be simple piping seams. If you Google 'piping seam', you can find pictures and even videos how they are actually made and see that it is basically exactly what is sounds like - just a pipe going around, that is sewed into the seam to hide it. 

I would recommend to model furniture with correct peaces of fabric so there will be seams on your models in the places there would be seams in reality. This helps with texturing and if you have UV seams already marked it is very easy to select them in edit mode with shift+g > Seams. Once selected you can duplicate them with shift+d and separate them with p > Selection. Then you can hit alt+c and convert the edges to curves. Once you have curves it is very easy to make pipes out of them just adding some bevel and adjusting it's resolution in the curve tab in the Properties Editor: 



You could also use another curve as a bevel object if you needed a more complex form. Also because you now have them as curves, you can use more complex geometry and deform it with Curve modifier to follow the shapes of these curves. This way you can model various complex patterns for classical furniture: